For exercise, solve the equations and inequalities. Write the solutions sets to

Jason Farmer

Jason Farmer

Answered question

2021-10-08

For exercise, solve the equations and inequalities. Write the solutions sets to the inequalities in interval notation if possible.
5x(x3)22+x0

Answer & Explanation

SabadisO

SabadisO

Skilled2021-10-09Added 108 answers

Step 1
To solve the following inequality:
5x(x3)22+x0
Step 2
Calculation:
Since, 5x(x3)22+x0
Multiplying both sides by -1, we get
5x(x3)22+x0
Dividing both sides by 5, we get,
x(x3)22+x0
The critical points are x=0,x=2,x=3
Step 3
Sign of x(x3)22+x can be summarized in the following table.
Range of xSign of x(x3)22+xx<2positivex=2not defined2<x<0negativex=0zero0<x<3positivex=3zerox>3positive
Hence, x(x3)22+x0 is satisfied when x<2,x=0,0<x<3,x>3
Therefore, given inequality is satisfied is x<2 and x0
Hence, given inequality is satisfied if x(2,0][0,)

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